Chapter 12
LOADS AND LOAD FACTORS
NDOT STRUCTURES MANUAL
September 2008
LOADS AND LOAD FACTORS
September 2008
Table of Contents
Section
12.1
Page
GENERAL ............................................................................................................... 12-1
12.1.1
Load Definitions........................................................................................ 12-1
12.1.1.1
12.1.1.2
12.1.2
Limit States............................................................................................... 12-3
12.1.2.1
12.1.2.2
12.1.3
Strength Load Combinations .................................................. 12-4
Service Load Combinations .................................................... 12-5
Extreme-Event Load Combinations ........................................ 12-6
Fatigue-and-Fracture Load Combination ................................ 12-6
Application of Multiple-Valued Load Factors........................... 12-6
PERMANENT LOADS ............................................................................................ 12-8
12.2.1
12.2.2
General..................................................................................................... 12-8
Deck Slab Dead Load............................................................................... 12-8
12.2.2.1
12.2.2.2
12.2.2.3
12.2.3
12.2.4
12.2.5
12.3
Basic LRFD Equation ............................................................. 12-3
Load Modifier .......................................................................... 12-4
Load Factors and Combinations............................................................... 12-4
12.1.3.1
12.1.3.2
12.1.3.3
12.1.3.4
12.1.3.5
12.2
Permanent Loads ................................................................... 12-1
Transient Loads ...................................................................... 12-2
General ................................................................................... 12-8
Composite Girders .................................................................. 12-8
Cast-in-Place Concrete Boxes................................................ 12-8
Distribution of Dead Load to Girders ........................................................ 12-9
Downdrag on Deep Foundations.............................................................. 12-9
Differential Settlement .............................................................................. 12-9
TRANSIENT LOADS............................................................................................... 12-10
12.3.1
12.3.2
General..................................................................................................... 12-10
Vehicular Live Load (LL)........................................................................... 12-10
12.3.2.1
12.3.2.2
12.3.2.3
12.3.2.4
12.3.2.5
12.3.2.6
12.3.2.7
12.3.2.8
12.3.2.9
12.3.2.10
12.3.2.11
General ................................................................................... 12-10
The Nature of the Notional Load............................................. 12-10
Multiple Presence Factors ...................................................... 12-11
Application of Vehicles and Lanes .......................................... 12-11
Special Load Applications....................................................... 12-12
Wheel Load for Deck Design .................................................. 12-14
Permit Loads for Design (P Load)........................................... 12-14
Fatigue Loads ......................................................................... 12-14
Distribution of Live Load to Piers ............................................ 12-16
Sidewalk Loading.................................................................... 12-20
Vehicular Collision Force (CT) ................................................ 12-20
12-i
LOADS AND LOAD FACTORS
September 2008
Table of Contents
(Continued)
Section
12.3.3
12.3.4
12.3.5
12.3.6
12-ii
Page
Friction Forces (FR).................................................................................. 12-20
Thermal Loads.......................................................................................... 12-21
Earthquake Effects ................................................................................... 12-21
Live-Load Surcharge (LS) ........................................................................ 12-22
LOADS AND LOAD FACTORS
September 2008
Chapter 12
LOADS AND LOAD FACTORS
Sections 1 and 3 of the LRFD Bridge Design Specifications discuss various aspects of loads.
Unless noted otherwise in Chapter 12 of the NDOT Structures Manual, the LRFD Specifications
applies to loads and load factors in Nevada. Chapter 12 also presents additional information on
NDOT practices.
12.1
GENERAL
12.1.1 Load Definitions
Reference:
LRFD Article 3.3.2
12.1.1.1 Permanent Loads
Reference:
LRFD Article 3.5
Permanent loads are loads that are always present in or on the bridge and do not change in
magnitude during the life of the bridge. Specific permanent loads include:
1.
2.
Gravitational Dead Loads.
•
DC – dead load of all of the components of the superstructure and substructure,
both structural and non-structural.
•
DW – dead load of additional non-integral wearing surfaces, future overlays and
any utilities crossing the bridge.
•
EL – accumulated lock-in, or residual, force effects resulting from the
construction process, including the secondary forces from post-tensioning (which
are not gravitational dead loads).
•
EV – vertical earth pressure from the dead load of earth fill.
Earth Pressures.
Reference:
LRFD Article 3.11
•
EH – horizontal earth pressure.
•
ES – earth pressure from a permanent earth surcharge (e.g., an embankment).
•
DD – loads developed along the vertical sides of a deep-foundation element
tending to drag it downward typically due to consolidation of soft soils underneath
embankments reducing its resistance.
12-1
LOADS AND LOAD FACTORS
September 2008
12.1.1.2 Transient Loads
Transient loads are loads that are not always present in or on the bridge or change in
magnitude during the life of the bridge. Specific transient loads include:
1.
Live Loads.
Reference:
2.
•
LL – static vertical gravity loads due to vehicular traffic on the roadway.
•
PL – vertical gravity loads due to pedestrian traffic on sidewalks.
•
IM – dynamic load allowance to amplify the force effects of statically applied
vehicles to represent moving vehicles, traditionally called impact.
•
LS – horizontal earth pressure from vehicular traffic on the ground surface above
an abutment or wall.
•
BR – horizontal vehicular braking force.
•
CE – horizontal centrifugal force from vehicles on a curved roadway.
Water Loads.
Reference:
•
3.
LRFD Article 3.7
WA – pressure due to differential water levels, stream flow or buoyancy.
Wind Loads.
Reference:
4.
LRFD Article 3.6
LRFD Article 3.8
•
WS – horizontal and vertical pressure on superstructure or substructure due to
wind.
•
WL – horizontal pressure on vehicles due to wind.
Extreme Events.
•
EQ – loads due to earthquake ground motions.
Reference:
•
CT – horizontal impact loads on abutments or piers due to vehicles or trains.
Reference:
•
LRFD Article 3.6.5
CV – horizontal impact loads due to aberrant ships or barges.
Reference:
12-2
LRFD Article 3.10
LRFD Article 3.14
LOADS AND LOAD FACTORS
•
IC – horizontal static and dynamic forces due to ice action.
Reference:
5.
September 2008
LRFD Article 3.9
Superimposed Deformations.
Reference:
6.
LRFD Article 3.12
•
TU – uniform temperature change due to seasonal variation.
•
TG – temperature gradient due to exposure of the bridge to solar radiation.
•
SH – differential shrinkage between different concretes or concrete and nonshrinking materials, such as metals and wood.
•
CR – creep of concrete or wood.
•
SE – the effects of settlement of substructure units on the superstructure.
Friction Forces.
Reference:
•
LRFD Article 3.13
FR – frictional forces on sliding surfaces from structure movements.
12.1.2 Limit States
Reference:
LRFD Article 1.3.2
The LRFD Specifications groups the traditional design criteria together within groups termed
“limit states.” The LRFD Specifications assigns load combinations to the various limit states.
12.1.2.1 Basic LRFD Equation
Components and connections of a bridge are designed to satisfy the basic LRFD equation for all
limit states:
∑ η γ Q ≤ φR
i
i
i
n
(LRFD Eq. 1.3.2.1-1)
Where:
γi
Qi
φ
Rn
ηi
=
=
=
=
=
load factor
load or force effect
resistance factor
nominal resistance
load modifier as defined in LRFD Equations 1.3.2.1-2 and 1.3.2.1-3
The left-hand side of LRFD Equation 1.3.2.1-1 is the sum of the factored load (force) effects
acting on a component; the right-hand side is the factored nominal resistance of the component.
The Equation must be considered for all applicable limit state load combinations. Similarly, the
Equation is applicable to superstructures, substructures and foundations.
12-3
LOADS AND LOAD FACTORS
September 2008
For the Strength limit states, the LRFD Specifications is basically a hybrid design code in that
the force effect on the left-hand side of the LRFD Equation is based upon elastic structural
response, while resistance on the right-hand side of the Equation is determined predominantly
by applying inelastic response principles. The LRFD Specifications has adopted the hybrid
nature of strength design on the assumption that the inelastic component of structural
performance will always remain relatively small because of non-critical redistribution of force
effects. This non-criticality is assured by providing adequate redundancy and ductility of the
structures, which is NDOT’s general policy for the design of bridges.
12.1.2.2 Load Modifier
The load modifier ηi relates the factors ηD, ηR and ηi to ductility, redundancy and operational
importance. The location of ηi on the load side of the LRFD Equation may appear
counterintuitive because it appears to be more related to resistance than to load. ηi is on the
load side for a logistical reason. When ηi modifies a maximum load factor, it is the product of
the factors as indicated in LRFD Equation 1.3.2.1-2; when ηi modifies a minimum load factor, it
is the reciprocal of the product as indicated in LRFD Equation 1.3.2.1-3. These factors are
somewhat arbitrary; their significance is in their presence in the LRFD Specifications and not
necessarily in the accuracy of their magnitude. The LRFD factors reflect the desire to promote
redundant and ductile bridges.
NDOT uses ηi values of 1.00 for all limit states, because bridges designed in accordance with
the NDOT Structures Manual will demonstrate traditional levels of redundancy and ductility.
Rather than penalize less redundant or less ductile bridges, such bridges are not encouraged.
NDOT may on a case-by-case basis designate a bridge to be of special operational importance
and specify an appropriate value of ηi.
The load modifier accounting for importance of LRFD Article 1.3.5, ηI, should not be confused
with the importance categories for seismic design of LRFD Articles 3.10.3 and 4.7.4.3. The
importance load modifier is used in the basic LRFD Equation, but the importance categories are
used to determine the minimum seismic analysis requirements.
12.1.3 Load Factors and Combinations
Reference:
LRFD Article 3.4.1
LRFD Table 3.4.1-1 provides the load factors for all of the load combinations of the LRFD
Specifications.
12.1.3.1 Strength Load Combinations
The load factors for the Strength load combinations are calibrated based upon structural
reliability theory and represent the uncertainty of their associated loads. The significance of the
Strength load combinations can be simplified as follows:
1.
12-4
Strength I Load Combination. This load combination represents random traffic and the
heaviest truck to cross the bridge in its 75-year design life. During this live-load event, a
significant wind is not considered probable.
LOADS AND LOAD FACTORS
September 2008
2.
Strength II Load Combination. In the LRFD Specifications, this load combination
represents an owner-specified permit load model. This live-load event has less
uncertainty than random traffic and, thus, a lower live-load load factor. This load
combination is used for design in conjunction with the permit live load design vehicle (P
loads) discussed in Section 12.3.2.7
3.
Strength III Load Combination. This load combination represents the most severe wind
during the bridge’s 75-year design life. During this severe wind event, no significant live
load is assumed to cross the bridge.
4.
Strength IV Load Combination. This load combination represents an extra safeguard for
bridge superstructures where the unfactored dead load exceeds seven times the
unfactored live load. Thus, the only significant load factor would be the 1.25 dead-load
maximum load factor. For additional safety, and based solely on engineering judgment,
the LRFD Specifications has arbitrarily increased the load factor for DC to 1.5. This load
combination need not be considered for any component except a superstructure
component, and never where the unfactored dead-load force effect is less than seven
times the unfactored live-load force effect. This load combination typically governs only
for longer spans, approximately greater than 200 ft in length. Thus, this load
combination will only be necessary in relatively rare cases.
5.
Strength V Load Combination. This load combination represents the simultaneous
occurrence of a “normal” live-load event and a “55-mph” wind event with load factors of
1.35 and 0.4, respectively.
For components not traditionally governed by wind force effects, the Strength III and Strength V
load combinations should not govern. Generally, the Strength I and Strength II load
combinations will govern for a typical multi-girder highway bridge.
12.1.3.2 Service Load Combinations
Unlike the Strength load combinations, the Service load combinations are material dependent.
The following applies:
1.
Service I Load Combination. This load combination is applied for controlling cracking in
reinforced concrete components and compressive stresses in prestressed concrete
components.
This load combination is also used to calculate deflections and
settlements of superstructure and substructure components.
2.
Service II Load Combination. This load combination is applied for controlling permanent
deformations of compact steel sections and the “slip” of slip-critical (i.e., friction-type)
bolted steel connections.
3.
Service III Load Combination. This load combination is applied for controlling tensile
stresses in prestressed concrete superstructure components under vehicular traffic
loads. The Service III load combination need not apply to the design permit live load
design vehicle.
4.
Service IV Load Combination. This load combination is applied for controlling tensile
stresses in prestressed concrete substructure components under wind loads. For
components not traditionally governed by wind effects, this load combination should not
govern.
12-5
LOADS AND LOAD FACTORS
September 2008
12.1.3.3 Extreme-Event Load Combinations
The Extreme-Event limit states differ from the Strength limit states, because the event for which
the bridge and its components are designed has a greater return period than the 75-year design
life of the bridge (or a much lower frequency of occurrence than the loads of the Strength limit
state). The following applies:
1.
Extreme-Event I Load Combination. This load combination is applied to earthquakes.
Because of the high seismicity in specific regions of Nevada, this load combination often
governs design. Earthquakes in conjunction with scour (which is considered a change in
foundation condition, not a load) can result in a very costly design solution if severe
scour is anticipated. In this case, NDOT practice is to combine one-half of the total
design scour (sum of contraction, local and long-term scour) with the full seismic loading.
2.
Extreme-Event II Load Combination. This load combination is applied to various types
of collisions (vessel, vehicular or ice) applied individually.
12.1.3.4 Fatigue-and-Fracture Load Combination
The Fatigue-and-Fracture load combination, although strictly applicable to all types of
superstructures, only affects the steel elements, components and connections of a limited
number of steel superstructures. Chapter 15 discusses fatigue and fracture for steel.
12.1.3.5 Application of Multiple-Valued Load Factors
12.1.3.5.1 Maximum and Minimum Permanent-Load Load Factors
In LRFD Table 3.4.1-1, the variable γP represents load factors for all of the permanent loads,
shown in the first column of load factors. This variable reflects that the Strength and ExtremeEvent limit state load factors for the various permanent loads are not single constants, but they
can have two extreme values. LRFD Table 3.4.1-2 provides these two extreme values for the
various permanent load factors, maximum and minimum. Permanent loads are always present
on the bridge, but the nature of uncertainty is that the actual loads may be more or less than the
nominal specified design values. Therefore, maximum and minimum load factors reflect this
uncertainty.
The designer should select the appropriate maximum or minimum permanent-load load factors
to produce the more critical load effect. For example, in continuous superstructures with
relatively short-end spans, transient live load in the end span causes the bearing to be more
compressed, while transient live load in the second span causes the bearing to be less
compressed and perhaps lift up. To check the maximum compression force in the bearing,
place the live load in the end span and use the maximum DC load factor of 1.25 for all spans.
To check possible uplift of the bearing, place the live load in the second span and use the
minimum DC load factor of 0.90 for all spans.
Superstructure design uses the maximum permanent-load load factors almost exclusively, with
the most common exception being uplift of a bearing as discussed above. The AASHTO
Standard Specifications treated uplift as a separate load combination. With the introduction of
maximum and minimum load factors, the LRFD Specifications has generalized load situations
such as uplift where a permanent load (in this case a dead load) reduces the overall force effect
(in this case a reaction). Permanent load factors, either maximum or minimum, must be
selected for each load combination to produce extreme force effects.
12-6
LOADS AND LOAD FACTORS
September 2008
Substructure design routinely uses the maximum and minimum permanent-load load factors
from LRFD Table 3.4.1-2. An illustrative yet simple example is a spread footing supporting a
cantilever retaining wall. When checking bearing, the weight of the soil (EV) over the heel is
factored up by the maximum load factor, 1.35, because greater EV increases the bearing
pressure, qult, making the limit state more critical. When checking sliding, EV is factored by the
minimum load factor, 1.00, because lesser EV decreases the resistance to sliding, Qτ, again
making the limit state more critical. The application of these maximum and minimum load
factors is required for foundation and substructure design; see Chapters 17 and 18.
12.1.3.5.2 Load Factors for Superimposed Deformations
The load factors for the superimposed deformations (TU, CR, SH) for the Strength limit states
also have two specified values ⎯ a load factor of 0.5 for the calculation of stress, and a load
factor of 1.2 for the calculation of deformation. The greater value of 1.2 is used to calculate
unrestrained deformations (e.g., a simple span expanding freely with rising temperature). The
lower value of 0.5 for the elastic calculation of stress reflects the inelastic response of the
structure due to restrained deformations. For example, one-half of the temperature rise would
be used to elastically calculate the stresses in a constrained structure. Using 1.2 times the
temperature rise in an elastic calculation would overestimate the stresses in the structure. The
structure resists the temperature inelastically through redistribution of the elastic stresses.
12-7
LOADS AND LOAD FACTORS
12.2
September 2008
PERMANENT LOADS
12.2.1 General
Reference:
LRFD Article 3.5
The LRFD Specifications specifies seven components of permanent loads, which are either
direct gravity loads or caused by gravity loads. The primary forces from prestressing are
considered to be part of the resistance of a component and has been omitted from the list of
permanent loads in Section 3 of the LRFD Specifications. However, when designing
anchorages for prestressing tendons, the prestressing force is the only load effect, and it should
appear on the load side of the LRFD Equation. The permanent load EL includes secondary
forces from pre-tensioning or post-tensioning. As specified in LRFD Table 3.4.1-2, use a
constant load factor of 1.0 for both maximum and minimum load factors for EL.
As discussed in Section 12.1.3.5.1, the permanent force effects in superstructure design are
factored by the maximum permanent-load load factors almost exclusively, with the most
common exception being the check for uplift of a bearing. In substructure design, the
permanent force effects are routinely factored by the maximum or minimum permanent-load
load factors from LRFD Table 3.4.1-2 as appropriate.
12.2.2 Deck Slab Dead Load
12.2.2.1 General
Loads applied to the composite cross section (i.e., the girder with the slab over it) include the
weight of any raised median, rail, sidewalk or barrier placed after the deck concrete has
hardened. Include a uniform load of 38 psf to account for a wearing surface over the entire
deck area between the face of rails or sidewalks.
12.2.2.2 Composite Girders
Reference:
LRFD Articles 6.10.1.1.1 and 9.7.4
Bridge deck slab dead load (DL) for design consists of composite and non-composite
components. Loads applied to the non-composite cross section (i.e., the girder alone) include
the weight of the plastic concrete, forms and other construction loads typically required to place
the deck. Calculate the non-composite DL using the full-slab volume including haunches.
Where steel stay-in-place formwork is used, the designer shall account for the steel form weight
and any additional concrete in the flutes of the formwork. The combined weight of the form and
concrete in the flutes shall not exceed 15 psf.
12.2.2.3 Cast-in-Place Concrete Box Girders
The designer shall account for the weight of lost deck forms by including an additional load of 12
psf.
12-8
LOADS AND LOAD FACTORS
September 2008
12.2.3 Distribution of Dead Load to Girders
Reference:
LRFD Article 4.6.2.2.1
For the distribution of the weight of plastic concrete to the girders, including that of an integral
sacrificial wearing surface, assume that the formwork is simply supported between interior
girders and cantilevered over the exterior girders.
Superimposed dead loads (e.g., curbs, barriers, sidewalks, parapets, railings, future wearing
surfaces) placed after the deck slab has cured may be distributed equally to all girders as
traditionally specified by AASHTO except for girder bridges with more than six girders. For
wider bridges with more than six girders, assume that the superimposed dead loads of
sidewalks, parapets or railings are carried by the three girders immediately under and adjacent
to the load. In some cases, such as staged construction and heavier utilities, the bridge
designer should conduct a more refined analysis, as discussed in Section13.2, to determine a
more accurate distribution of superimposed dead loads.
For cast-in-place concrete box girders, assume equal distribution across the full bridge deck
width.
12.2.4 Downdrag on Deep Foundations
Reference:
LRFD Article 3.11
Deep foundations (i.e., driven piles and drilled shafts) through unconsolidated soil layers may be
subject to downdrag, DD. Downdrag is a load developed along the vertical sides of a deepfoundation element tending to drag it downward typically due to consolidation of soft soils
underneath embankments reducing its resistance. Calculate this additional load as a skinfriction effect. If possible, the bridge designer should detail the deep foundation to mitigate the
effects of downdrag; otherwise, it is necessary to design considering downdrag. Section
17.3.3.1 discusses mitigation methods.
12.2.5 Differential Settlement
Differential settlement between adjacent substructure units or transversely across a single
substructure unit induces stresses in continuous structures and deflections in simple structures.
Although most bridges can easily resist these stresses and deflections, the potential effects of
differential settlement should be considered for all structures. The effects of differential
settlement in the longitudinal direction need not be considered if its magnitude is ½ in or less.
The effects of differential settlement in the transverse direction should be considered on a caseby-case basis.
12-9
LOADS AND LOAD FACTORS
12.3
September 2008
TRANSIENT LOADS
12.3.1 General
The LRFD Specifications recognizes 19 transient loads. Static water pressure, stream
pressure, buoyancy and wave action are integrated as water load, WA. Creep, settlement,
shrinkage and temperature (CR, SE, SH, TU and TG) are elevated in importance to “loads,”
being superimposed deformations which, if restrained, will result in force effects. For example,
restrained strains due to uniform-temperature increase induces compression forces. The LRFD
Specifications has considerably increased the vehicular braking force (BR) to reflect the
improvements in the mechanical capability of modern trucks in comparison with the traditional
values of the AASHTO Standard Specifications.
12.3.2 Vehicular Live Load (LL)
12.3.2.1 General
Reference:
LRFD Articles 3.6.1.1, 3.6.1.2 and 3.6.1.3
For short and medium span bridges, which predominate in Nevada, vehicular live load is the
most significant component of load. Dead loads become more significant for long-span bridges.
Long-span bridges are defined as those governed by the Strength IV load combination where
the dead load is seven times or more greater than the live load.
12.3.2.2 The Nature of the Notional Load
The HL-93 live-load model is a notional load in that it is not a true representation of actual truck
weights. Instead, the force effects (i.e., the moments and shears) due to the superposition of
vehicular and lane load within a single design lane are a true representation of the force effects
due to actual trucks.
The components of the HL-93 notional load are:
•
a vehicle, either the familiar HS-20 truck, now called the design truck, or a 50-kip design
tandem, similar to the Alternate Loading, both of the Standard Specifications; and
•
a 0.64 k/ft uniformly distributed lane load, similar to the lane load of the Standard
Specifications, but without any of the previous associated concentrated loads.
Note that the dynamic load allowance (IM) of 0.33 is applicable only to the design trucks and the
design tandems, but not to the uniformly distributed lane load.
The force effects of the traditional HS-20 truck alone are less than that of the legal loads. Thus,
a heavier vehicle is appropriate for design. As specified for the HL-93 live-load model, the
concept of superimposing the design vehicle force effects and the design lane force effects was
developed to yield moments and shears representative of real trucks on the highways. The
moments and shears produced by the HL-93 load model are essentially equivalent to those of a
57-ton truck.
12-10
LOADS AND LOAD FACTORS
September 2008
12.3.2.3 Multiple Presence Factors
The multiple presence factor of 1.0 for two loaded lanes, as given in LRFD Table 3.6.1.1.2-1, is
the result of the LRFD Specifications’ calibration for the notional load, which has been
normalized relative to the occurrence of two side-by-side, fully correlated, or identical, vehicles.
The multiple presence factor of 1.2 for one loaded lane should be used where a single design
tandem or single design truck governs, such as in overhangs, decks, etc. The multiplepresence factors should not be applied to fatigue loads.
12.3.2.4 Application of Vehicles and Lanes
The LRFD Specifications retains the traditional design lane width of 12 ft and the traditional
spacing of the axles and wheels of the HS-20 truck. Both vehicles (the design truck and design
tandem) and the lane load occupy a 10-ft width placed transversely within the design lane for
maximum effect, as specified in LRFD Article 3.6.1.3 and illustrated schematically in Figure
12.3-A.
PLACEMENT OF THE DESIGN LOADS WITHIN THE DESIGN LANES
Figure 12.3-A
12-11
LOADS AND LOAD FACTORS
September 2008
12.3.2.5 Special Load Applications
12.3.2.5.1 Two Design Trucks in a Single Lane for Negative Moment and Interior
Reactions
Reference:
LRFD Article 3.6.1.3.1
The combination of the lane load and a single vehicle (either a design truck or a design tandem)
does not always adequately represent the real-life loading of two heavy vehicles closely
following one another, interspersed with other lighter traffic. Thus, a special load case has been
specified in the LRFD Specifications to calculate these force effects. Two design trucks, with a
fixed rear axle spacing of 14 ft and a clear distance not less than 50 ft between them,
superimposed upon the lane load, all within a single design lane and adjusted by a factor of
0.90 approximates a statistically valid representation of negative moment and interior reactions
due to closely spaced heavy trucks. This sequence of highway loading is specified for negative
moment and reactions at interior piers due to the shape of the influence lines for such force
effects. This sequence is not extended to other structures or portions of structures because it is
not expected to govern for other influence-line shapes. This loading is illustrated in Figure
12.3-B.
In positioning the two trucks to calculate negative moment or the interior reaction over an
internal support of a continuous girder, spans should be at least 90 ft in length to be able to
position a truck in each span’s governing position (over the peak of the influence line). If the
spans are larger than 90 ft in length, the trucks remain in the governing positions but, if they are
smaller than 90 ft, the maximum force effect can only be attained by trial-and-error with either
one or both trucks in off-positions (i.e., non-governing positions for each individual span away
from the peak of the influence line). These effects are illustrated in Figure 12.3-C.
12.3.2.5.2 Application of Horizontal Superstructure Forces to the Substructure
The transfer of horizontal superstructure forces to the substructure depends on the type of
superstructure to substructure connection. Centrifugal force (CE), braking force (BR) and wind
on live load (WL) are all assumed to act horizontally at a distance of 6 ft above the roadway.
Connections can be fixed, pinned or free for both moment and shear.
SPECIAL LOADING FOR NEGATIVE MOMENT AND
INTERIOR REACTIONS OF CONTINUOUS SPANS
Figure 12.3-B
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LOADS AND LOAD FACTORS
12-13
Figure 12.3-C
September 2008
APPLICATION OF DESIGN VEHICULAR LIVE LOAD – LRFD ARTICLE 3.6.1.3
LOADS AND LOAD FACTORS
September 2008
If the horizontal superstructure force is being applied to the substructure through a pinned
connection, there is no moment transfer. The designer should apply the superstructure force to
the substructure at the connection.
For a fixed or moment connection, apply the superstructure horizontal force with an additional
moment to the substructure. The additional moment is equal to the horizontal force times the
distance between the force’s line of action and the point of application.
12.3.2.6 Wheel Load for Deck Design
Reference:
LRFD Article 3.6.1.3.3
Bridge decks shall be designed to carry axles consisting of two 20-kip wheels with dynamic
allowance, alone or in combination with the lane load as appropriate. This axle load is
consistent with the HS-25 truck.
12.3.2.7 Permit Loads for Design (P Load)
NDOT has adopted one of the Caltrans “Standard Permit Design Vehicles” for the design of
structures to provide a minimum permit-load capacity on all highway structures to account for
vehicles that exceed the legal limits and that operate on highways and structures under special
transportation permits. This load is commonly called the “P” load. Typically, all State-owned
bridges are designed for the Strength II, Service I and Service II load combinations with the P
load in all lanes. The application of the P load to non-State owned bridges is determined on a
case-by-case basis.
The P load, specifically the Caltrans P-13, is illustrated in Figure 12.3-D.
12.3.2.8 Fatigue Loads
Reference:
LRFD Articles 3.6.1.4.1, 3.6.1.4.2
The LRFD Specifications defines the fatigue load for a particular bridge component by
specifying both a magnitude and a frequency. The magnitude of the fatigue load consists of a
single design truck per bridge with a load factor of 0.75 (i.e., the factored force effects are
equivalent to those of an HS-15 truck). This single-factored design truck produces a
considerable reduction in the stress range in comparison with the stress ranges of the AASHTO
Standard Specifications. However, fatigue designs using the LRFD Specifications are virtually
identical to those of the Standard Specifications. This equivalence is accomplished through an
increase in the frequency from values on the order of two million cycles in the Standard
Specifications, which represented “design” cycles, to frequencies on the order of tens and
hundreds of millions of cycles, which represent actual cycles in the LRFD Specifications.
This change to more realistic stress ranges and cycles, illustrated in the S-N curve (a log-log
plot of stress range versus cycle to failure) of Figure 12.3-E, increases the designer’s
understanding of the extremely long fatigue lives of steel bridges. In Figure 12.3-E, S1
represents the controlling stress range for multiple lanes of strength-magnitude loading typically
in accordance with the Standard Specifications, with N1 being its corresponding number of
design cycles. S2 represents the controlling stress range for a single fatigue truck in accordance
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LOADS AND LOAD FACTORS
September 2008
PERMIT DESIGN LIVE LOADS
(For P-13 Vehicle)
Figure 12.3-D
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LOADS AND LOAD FACTORS
September 2008
COMPARISON OF THE FATIGUE LOADS OF THE LRFD SPECIFICATIONS AND
STANDARD SPECIFICATIONS
Figure 12.3-E
with the LRFD Specifications, with N2 being its corresponding number of actual cycles. The
increase in the number of cycles compensates for the reduction in stress range, yet both cases
fall on the resistance curve producing a similar fatigue design.
The bridge designer shall also apply P loads, also with a load factor of 0.75, to the fatigue
design for structural steel. In lieu of better information, the average daily truck traffic in a single
lane, ADTTSL, for the P load shall be taken as 10 trucks per day.
12.3.2.9 Distribution of Live Load to Piers
Reference:
LRFD Article 3.6.1.3.1
To promote uniformity of distribution of live load to piers and other substructure components, the
following procedure is suggested unless a more exact distribution of loads is used:
1.
Live-Load Distribution Factor. The live-load distribution factor for each girder shall be
determined assuming that the deck is acting as a simple girder between interior girders
and as a cantilever spanning from the first interior girder over the exterior girder.
2.
Live Load on Design Lanes. Design lanes shall be placed on the bridge to produce the
maximum force effect for the component under investigation. Separate loadings of the
HL-93 live load or the P load shall be placed within an individual design lane to likewise
produce the maximum effect. The bridge designer shall consider one, two, three or
more design lanes in conjunction with the multiple presence factors of LRFD Table
3.6.1.1.2-1, as can be accommodated on the roadway width.
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LOADS AND LOAD FACTORS
3.
September 2008
Reaction on Piers. For piers with drop caps, live loads are transmitted to the pier
through the girder bearings, and the cap shall be designed using the shears determined
from the girder line analysis. For integral caps, the designer may distribute the live load
to the cap using a wheel line method, a girder and axle method, or a combination of the
two. The wheel line method and the girder and axle method are described in Example
12.3-1. For both drop caps and integral caps, the designer shall analyze multiple lane
positions to maximize load effects (e.g., side-by-side lanes to maximize negative cap
bending at an interior pier support, lanes placed in every other cap span to maximize
positive bending).
**********
Example 12.3-1 ⎯ Live Load Placement on Integral Bent Caps
Given:
•
Two-span bridge, 145-ft and 160-ft spans, zero skew, box girder depth of 6′-6″
•
Girder spacing = 9′-4″
•
Column Spacing = 18′8″ (with zero skew, pier is normal to bridge centerline)
•
From the superstructure analysis, the reaction at the center pier for a single
HL-93 lane with both spans loaded was determined to be 200k
•
HL-93 loading is depicted in this example. Treat permit loads in a similar
fashion. Apply superstructure dead load to the integral cap at girder lines
a.
Wheel Line Method (Simplified Approach)
Determine wheel line loads from HL-93 lane reaction:
WHL-93 =
=
½ (lane reaction)
½ (220k) = 110 k
Wheel lines are applied 6 ft apart in a lane and 4 ft apart between lanes. As
positioned in Figure 12.3-F(a), wheel lines are located to maximize positive
bending in the cap beam. Analyze additional wheel line patterns to maximize
load effects along the length of the cap beam (i.e., to develop moment and
shear envelopes). A “train” of wheel lines running across the cap as a moving
load is an easy approach to generating the envelopes.
b.
Girder and Axle Method (Refined Approach)
This refined approach recognizes that the majority of the lane load is
transferred to the cap through the girder lines while a portion of the lane load
could be positioned anywhere on the cap as an axle passes over. To
represent this condition, the lane loading is divided between that which reaches
the cap through the girders and that which is caused by the heaviest axle from
the design vehicle applied directly to the cap. Determine the loads to girders
assuming that the deck is simply supported between girder lines. From the full
lane load, subtract the heaviest vehicle axle for direct application to the pier
cap.
Figure 12.3-G represents girder and axle load placement to produce maximum
positive bending in the cap. From statics:
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LOADS AND LOAD FACTORS
12-18
Figure 12.3-F
September 2008
LIVE LOAD APPLICATION
(Integral Cap)
LOADS AND LOAD FACTORS
12-19
Figure 12.3-G
September 2008
PARTIAL CAP ELEVATION
LOADS AND LOAD FACTORS
G2
=
September 2008
G3
=
=
=
W + 6W/9.33 + 2W/9.33
1.86W
0.93 lanes
HL-93 axle
G2 = G3
=
=
=
32k
0.93 (220k – 32k)
175k
See Figure 12.3-F(b) for placement of loads across the integral cap.
**********
12.3.2.10 Sidewalk Loading
Reference:
LRFD Article 3.6.1.6
Where sidewalks are present on the bridge, the bridge designer shall design for the dead load
and pedestrian live load on the sidewalk; however, the full width of the bridge, including
sidewalks, shall also be designed for the traffic live load assuming that traffic can mount the
sidewalk.
Pedestrian and traffic loads will not be applied together. Sidewalks separated from traffic lanes
by barrier rail shall also be designed for vehicular loads due to the potential for future widening.
12.3.2.11 Vehicular Collision Force (CT)
Reference:
LRFD Article 3.6.5
Bridge abutments and piers over highways or railroads within a distance of:
•
•
30 ft to the edge of the roadway, or
50 ft to the centerline of the railroad track
shall be protected as specified in LRFD Article 3.6.5.1. If this is deemed to be impractical and
with the approval of the Chief Structures Engineer, the abutment or pier shall be designed for a
collision force of 400 kips acting in a horizontal plane in any direction at a distance of 4 ft above
ground, as specified in LRFD Article 3.6.5.2.
12.3.3 Friction Forces (FR)
Reference:
LRFD Article 3.13
LRFD Article 3.13 discusses the determination of horizontal friction forces from an expansion
bearing sliding on its bearing plate on the supporting substructure component.
The bridge designer should adjust the frictional forces from sliding bearings to account for
unintended additional friction forces due to the future degradation of the coefficient of friction of
the sliding surfaces. Consider the horizontal force due to friction conservatively. Include friction
forces where design loads would increase, but neglect friction forces where design loads would
decrease.
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LOADS AND LOAD FACTORS
September 2008
12.3.4 Thermal Loads
Reference:
LRFD Article 3.12.2
The bridge designer shall use Procedure A of LRFD Article 3.12.2.1 to determine the
appropriate design thermal range.
For Nevada-specific ranges of temperatures and
procedures, see Section 19.1.
12.3.5 Earthquake Effects
Reference:
LRFD Article 3.10
The seismic provisions of the LRFD Specifications shall be applied to bridge design in Nevada.
The seismicity of Nevada varies greatly across the State. Nevada includes all four seismic
zones specified in the LRFD Specifications. Earthquake force effects shall be determined in
accordance with LRFD Article 3.10; however, the minimum seismic coefficients shown in Figure
12.3-H shall be applied unless otherwise approved by the Chief Structures Engineer.
Other Chapters in the NDOT Structures Manual present NDOT’s seismic detailing practices.
For example, Chapter 15 presents NDOT’s seismic detailing practices for steel superstructures.
County
Peak Ground
Acceleration (PGA)
Coefficient
Short-Period
Spectral
Acceleration
Coefficient (Ss)
Long-Period
Spectral
Acceleration
Coefficient (Sl)
Carson City, Douglas,
Esmerelda, Washoe
0.50
1.25
0.50
Lyon, Mineral, Storey
0.40
1.00
0.40
Churchill, Nye
0.35
0.80
0.30
Eureka, Lander,
Lincoln, Pershing
0.25
0.60
0.20
Clark, Elko,
Humboldt, White Pine
0.15
0.40
0.15
MINIMUM SEISMIC COEFFICIENTS BY COUNTY
Figure 12.3-H
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LOADS AND LOAD FACTORS
September 2008
12.3.6 Live-Load Surcharge (LS)
Reference:
LRFD Article 3.11.6.2
Where reinforced concrete approach slabs are provided at bridge ends, live-load surcharge
need not be considered on the abutment; however, the bridge designer shall consider the
reactions on the abutment due to the axle loads on the approach slabs. Because approach
slabs are required at all bridges in Nevada, live-load surcharge is not used for abutments.
Retaining walls that retain soil supporting a roadway must be able to resist the lateral pressure
due to the live-load surcharge. See Section 23.1 for retaining walls.
12-22